### relativistic invariance

**(Lorentz invariance)**
(quantity that remains the same regardless of frame of reference)

**Relativistic invariance** (or **Lorentz invariance**) means
"the same regardless of frame of reference".
For example, a relativistic invariant quantity would be the same
if you measured it while you are at rest
versus if you measured it while you are moving at a constant velocity.
If it is a quantity requiring the
Lorentz transform when shifting frames of reference,
then the value of the quantity is unchanged by the transform,
and often the phrase *relativistic invariance*
is used specifically to mean that particular usage.

An example is the speed of light (c),
and the discovery of its invariance (through measurement)
was a prime motivator for the development of relativity
and the Lorentz transform.
Applying the transform to the speed of light
does indeed always yield the same value.
Mass (as the word is generally used, i.e., as the "rest mass") is
invariant, but only because, as defined, one doesn't apply the
Lorentz transform.

The terms are also used for laws of physics, i.e., equations, that
remain true in different frames of reference. Some familiar laws
are invariant, and some have *relativistic* versions that are
invariant, i.e., that make their point using only invariant quantities,
and some are "meta", e.g., the laws of relativity itself.

Lengths and time intervals are famously *not* invariant:
a foot-long ruler no longer measures to exactly a foot
when measured from a frame of reference in which the ruler is moving.
A **spacetime interval** (for two events happening some
distance and time interval apart, it is square root of the
difference between the distance squared and the time interval squared)
does remain unchanged under the Lorentz transform.
The *minimum time interval* or *minimum distance* between two events
(among all frames of reference) is also a fixed number, but that's
because such a minimum would occur in a specific frame of reference:
its lack of variation is because we've stepped back from comparing
multiple frames and are commenting on a property of a single
frame that is specific to that distance or interval.

(*physics,relativity*)
**Further reading:**

http://en.wikipedia.org/wiki/Lorentz_covariance

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/releng.html

**Referenced by pages:**

Lorentz transformation

metric

relativistic momentum

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